CHICAGO – While their first free-agent priority is hometowner Chris Webber, the Pistons are also plotting to make a run at another free-agent star with Detroit connections – Allan Houston, league officials told The Post.

The Pistons, Houston’s former team, are one of just a handful of teams that have the cap room to sign the Knicks’ All-Star shooting guard outright without a complicated sign-and-trade. Detroit is $17 million under the cap and would be willing to give him the maximum contract allowable under the collective bargaining agreement. Detroit’s entry in the hunt would be the worst nightmare for the Knicks, who would get no compensation for Houston as opposed to shipping Houston in a sign-and-trade.

Pistons president Joe Dumars is a former teammate of Houston’s and they still have a good relationship. Tamara, Houston’s wife, hails from the Detroit suburb of Bloomfield Hills.

Dumars and Piston officials are not allowed to contact Houston or his agent Bill Strickland until he becomes a free agent July 1. Dumars, who is on hand for the Chicago pre-draft camp, declined to comment on his interest in Houston, citing tampering charges.

However, a source close to Dumars said he is intrigued about the idea of bringing Houston back to Detroit, even though they have All-Star Jerry Stackhouse as their shooting guard and it would create the same sort of dilemma the Knicks face now with Houston and Latrell Sprewell. Piston fans have long forgiven Houston for his departure to the Knicks in the summer of 1996 after three seasons with in Detroit.

Houston has said repeatedly he wants to re-sign with the Knicks. Of his other options, the Pistons could be one place that would be an acceptable alternative. The under-the-cap Bulls also have interest in Houston but the Knicks guard is not interested in playing for a league doormat.

The Knicks want to sign Houston but are eager to attempt a sign-and-trade if the right deal for a star big man such as Webber comes along so as to ease their glut at the swingman position. (Houston would have to approve any sign-and-trade).

If Webber turns down Detroit, league sources said the Pistons also will try to be a third or fourth team along with Sacramento and the Knicks to facilitate a Webber blockbuster in which they might get a quality body for a draft choice to make the deal work under the cap. For instance, it’s been long speculated the Knicks and Sacramento will need a third team and possibly fourth team to make a Webber-to-the-Knicks deal work. The Kings don’t have a need for Houston and Houston doesn’t want to play in Sacramento.